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Physical Review A

Noise-induced fluctuations in two-ion systems driven by light beams

JORGE R. SOBEHART, Ricardo Farengo

Published Oct 1, 1995• 1 citation
Publisher

Abstract

The dynamics of a system composed of two strongly coupled ions trapped in a time-dependent potential well and cooled by a laser beam is studied. In the present classical treatment the photon-ion interaction is simulated with an effective noise acting on the ions, which produces a stochastic transfer of momentum. The existence of noise-induced fluctuations in the regime where previous analysis indicated that the two-ion system dynamics was stable is discussed.

DOI
10.1103/physreva.52.3022

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The dynamics of a system composed of two strongly coupled ions trapped in a time-dependent potential well and cooled by a laser beam is studied. In the present classical treatment the photon-ion interaction is simulated with an effective noise acting on the ions, which produces a stochastic transfer of momentum. The existence of noise-induced fluctuations in the regime where previous analysis indicated that the two-ion system dynamics was stable is discussed.
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We study the stochastic dynamics of a particle in a periodically driven potential. For atomic ions trapped in radio-frequency Paul traps, noise heating and laser cooling typically act slowly in comparison with the unperturbed motion. These stochastic processes can be accounted for in terms of a probability distribution defined over the action variables, which would otherwise be conserved within the regular regions of the Hamiltonian phase space. We present a semiclassical theory of low-saturation laser cooling applicable from the limit of low-amplitude motion to large-amplitude motion, accounting fully for the time-dependent and anharmonic trap. We employ our approach to a detailed study of the stochastic dynamics of a single ion, drawing general conclusions regarding the nonequilibrium dynamics of laser-cooled trapped ions. We predict a regime of anharmonic motion in which laser cooling becomes diffusive (i.e., it is equally likely to cool the ion as it is to heat it), and can also turn into effective heating. This implies that a high-energy ion could be easily lost from the trap despite being laser cooled; however, we find that this loss can be counteracted using a laser detuning much larger than Doppler detuning.
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We present a systematic semiclassical model for the simulation of the dynamics of a single two-level atom strongly coupled to a driven high-finesse optical cavity. From the Fokker-Planck equation of the combined atom-field Wigner function we derive stochastic differential equations for the atomic motion and the cavity field. The corresponding noise sources exhibit strong correlations between the atomic momentum fluctuations and the noise in the phase quadrature of the cavity field. The model provides an effective tool to investigate localisation effects as well as cooling and trapping times. In addition, we can continuously study the transition from a few photon quantum field to the classical limit of a large coherent field amplitude.